Phase contrast cardiac magnetic resonance imaging (PC-MRI) is widely used for the clinical in-vivo assessment of blood flow in the diagnosing of various diseases and the depiction of the vessels in the body. Through-plane aortic and pulmonic blood flow are measured and used for the evaluation of cardiac function and output, mitral regurgitation, and shunts. Clinically, a through-plane 2D image acquisition is performed for the evaluation of blood flow. 3D time-resolved PC image processing may be performed that allows quantification and visualization of the blood flow in all three directions. However, lengthy acquisition times have prevented the multi-directional PC techniques from coming into widespread usage.
A balanced four-point encoding (BFPE) is a commonly used encoding strategy for three-directional PC-MRI. In BFPE, each reconstructed frame corresponds to one of the four encodings. To save acquisition time, traditionally, four adjacent frames are processed together on a pixel-by-pixel basis to estimate the unknown phase (velocity). The processing is done by taking the four adjacent (in time) measurements and solving a set of 4×4 equations. If m1:4 represent the first four measurements, and E1:4 the first four encoding directions, {right arrow over (ϕ)}1 can be obtained by solving the equations.E1:4{right arrow over (ϕ)}1=m1:4 The window is moved by a step of 4 and the process is repeated for the next four measurements.E5:8{right arrow over (ϕ)}5=m5:8 
To improve temporal resolution, the sliding window approach is often used where the window is advanced by a step of one instead of four frames at a time. It allows reconstructing phase (velocity) at a temporal grid which is four times finer.E1:4{right arrow over (ϕ)}1=m1:4 E2:4{right arrow over (ϕ)}2=m2:5 
Although the standard sliding window approach may improve the apparent resolution, it often introduces strong oscillatory artifacts because the underlying assumption that the velocities do not change significantly during the timespan of four consecutive measurements is not always valid.